Negative thermal expansion in cubic ZrW2O8: Role of phonons in the entire Brillouin zone fromab initiocalculations

Abstract

We report the ab initio density functional theory calculation of phonons in the cubic phase of ZrW${}_{2}$O${}_{8}$ in the entire Brillouin zone and identify specific anharmonic phonons that are responsible for large negative thermal expansion (NTE) in terms of the translation, rotation, and distortion of WO${}_{4}$ and ZrO${}_{6}$. We have used density functional calculations to interpret the experimental phonon spectra as a function of pressure and temperature as reported in literature. We discover that the phonons showing anharmonicity with temperature are not necessarily the same as those showing anharmonicity with pressure although both are of similar frequencies. Only the latter phonons are associated with NTE. Therefore, the cubic and/or quadratic anharmonicity of phonons is not relevant to NTE but just the volume dependence of frequencies. The calculations are able to reproduce the observed anomalous trends, namely, the softening of the low-frequency peak at about 4 meV in the phonon spectra with pressure and its hardening with temperature, whereas, both changes involve a compression of the lattice.